Learning Manifolds in High-D Point Embedding for Anisotropic Surface Approximation from Unstructured Point Clouds

2026-07-30

AI Summary

This work addresses the challenges of geometric redundancy and real-time processing in dense point clouds by proposing HD-PEA, a framework designed to efficiently construct high-fidelity, geometrically aligned, and sparser anisotropic surface representations. The method maps input point clouds into a high-dimensional Euclidean embedding space, where it performs end-to-end surface reconstruction by integrating tangent subspace estimation with anisotropic optimization. HD-PEA innovatively introduces a block-wise meta-embedding inference mechanism and a Riemannian curvature tensor-guided anisotropic reconstruction strategy, enabling scalable processing of large-scale point clouds without retraining. Extensive experiments demonstrate that HD-PEA consistently outperforms state-of-the-art methods across multiple benchmarks—including Thingi10K, AIM@SHAPE, Stanford, and ScanNet—achieving superior performance in terms of surface fidelity, mesh compactness, numerical stability, and generalization capability.

Abstract

Dense 3D sensors in various real-world fields produce point clouds that are geometrically redundant for real-time processing. In this paper, we propose an efficient and scalable learning-based anisotropic surface approximation framework, HD-PEA, that operates directly on unstructured point clouds, integrating anisotropic optimization into reconstruction to produce compact, geometry-aligned surface representations with higher fidelity, fewer elements, and improved numerical stability compared to isotropic and adaptive meshes. Firstly, we develop a novel learning-based high-dimensional (high-d) Euclidean point embedding method to map the input point clouds into a high-d manifold embedding space. For handling large-scale point clouds without retraining and fine-tuning, a patch-based meta-embedding scheme is designed during the inference stage. Then, we develop a new tangent subspace estimation for the high-d embedding manifold approximation and anisotropic manifold reconstruction in high-d space. The main contribution of this work is to propose a scalable deep learning framework and a variety of datasets for constructing a high-d Euclidean point embedding space aimed to 3D anisotropic surface mesh approximation and Riemannian curvature tensor estimation from point clouds. We extensively evaluate our method against state-of-the-art surface reconstruction approaches using several datasets, such as Thingi10K dataset, AIM@SHAPE and Stanford 3D Scanning Repository, ScanNet dataset, and further demonstrate its generalization and usability on diverse unseen shapes and applications from these datasets.

Problem

• anisotropic surface approximation
• unstructured point clouds
• manifold learning
• 3D surface reconstruction
• high-dimensional embedding

Innovation

• high-dimensional embedding
• anisotropic surface approximation
• point cloud reconstruction
• manifold learning
• Riemannian curvature estimation